We present a model checking procedure for the CSL until operator on the CTMCs that underlie Jackson queueing networks. The key issue lies in the fact that the underlying CTMC is infinite in as many dimension as there are queues in the JQN. We need to compute the transient state probabilities for all goal states and for all possible starting states. However, for these transient probabilities no computational procedures are readily available. The contribution of this paper is the proposal of a new uniformization-based approach to compute the transient state probabilities. Furthermore, we show how the highly structured state space of JQNs allows us to compute the possible infinite satisfaction set for until formulas. A case study on an e-business site shows the feasibility of our approach.